Surface acoustic wave filter

ABSTRACT

A SAW filter includes a first SAW resonator having a pair of terminals and a predetermined resonance frequency (f rp ), the first SAW resonator being provided in a parallel arm of the SAW filter. A second SAW resonator has a pair of terminals and a predetermined resonance frequency (f rs ) approximately equal to a predetermined antiresonance frequency of the first SAW resonator (f ap ). The second SAW resonator is provided in a series arm of the SAW filter. An inductance element is connected in series to the first SAW resonator.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application No. 07/965,774, filedOct. 23, 1992, now U.S. Pat. No. 5,559,481, patented Sep. 24, 1996. Thisapplication and application Ser. No. 09/314,943, filed May 20, 1999 (nowU.S. Pat. No. RE 37,790 ), are each reissues of U.S. Pat. No. 5,631,612(application Ser. No. 08/369,492, filed Jan. 6, 1995 ). This applicationis a continuation of application Ser. No. 09/314,943, filed May 20,1999, now U.S. Pat. No. RE 37,390, the contents of which are herebyincorporated by reference, which is a reissue of U.S. Pat. No. 5,631,612(application Ser. No. 08/369,492, filed Jan. 6, 1995 ), which is acontinuation of application Ser. No. 07/965,774, filed Oct. 23, 1992,now U.S. Pat. No. 5,559,481. This application is related to applicationSer. No. 09/158,074, filed Sep. 22, 1998, now U.S. Pat. No. RE 37,375,which is a reissue of U.S. Pat. No. 5,559,481.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to surface acoustic wave (SAW)filters, and more particularly to a ladder-type SAW filter suitable foran RF (Radio Frequency) filter provided in pocket and mobile telephones,such as automobile phone sets and portable phones.

2. Description of the Prior Art

In Japan, an automobile phone or portable phone system has aspecification in which a transmission frequency band is ±8.5 MHz about acenter frequency of 933.5 MHz. The ratio of the above transmission bandto the center frequency is approximately 2%.

Recently, SAW filters have been employed in automobile phone or portablephone systems. It is required that the SAW filters have characteristicswhich satisfy the above specification. More specifically, it is requiredthat the pass band width is so broad that 1) the ratio of the pass bandto the center frequency is equal to or greater than 2%, 2) the insertionloss is small and equal to 5 dB−2 dB, and 3) the suppression factor ishigh and equal to 20 dB−30 dB.

In order to satisfy the above requirements, SAW filters are substitutedfor conventional transversal filters. Generally, SAW elements are soconnected that a ladder-type filter serving as a resonator is formed.

FIG. 1 is an equivalent circuit of a SAW filter disclosed in JapaneseLaid-Open Patent Publication No. 52-19044. A SAW filter 1 shown in FIG.1 comprises a SAW resonator 3 in a series arm 2, and a SAW resonator 5in a parallel arm 4. The equivalent parallel capacitance C_(OB) of theresonator 5 in the parallel arm 4 is larger than the equivalent parallelcapacitance C_(OA) of the resonator 3 in the series arm 2.

The SAW filter 1 shown in FIG. 1 has a characteristic shown in FIG. 2. Acurve 6 shows an attenuation quantity v. frequency characteristic of theSAW filter 1. As indicated by arrows 7 shown in FIG. 2, the suppressionfactor increases as the equivalent parallel capacitance C_(OB)increases. However, as the equivalent parallel capacitance C_(OB)increases, the band width decreases, as indicated by arrows 8, and theinsertion loss increases, as indicated by an arrow 9. Hence, thecharacteristic deteriorates, as indicated by a broken line 10. Whentrying to obtain a suppression factor equal to or larger than 20 dB, theband width is decreased to that the ratio of the pass band to the centerfrequency is equal to or smaller than 1%, and does not satisfy theaforementioned specification of the 800 MHz-band radio systems.

SUMMARY OF THE INVENTION

It is a general object of the present invention to provide a SAW filterin which the above disadvantages are eliminated.

A more specific object of the present invention is to provide a SAWfilter having a large band width, a large suppression factor, and asmall insertion loss.

The above objects of the present invention are achieved by a SAW filtercomprising: a first SAW resonator (21, R1A, R1B) having a pair ofterminals and a predetermined resonance frequency (f_(rp)), the firstSAW resonator being provided in a parallel arm (24) of the SAW filter; asecond SAW resonator (23) having a pair of terminals and a predeterminedresonance frequency (f_(rs)) approximately equal to the predeterminedantiresonance frequency of the first SAW resonator (f_(ap)), the secondSAW resonator being provided in a series arm (24) of the SAW filter; andan inductance element (25, L1) connected in series to the first SAWresonator.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention willbecome more apparent from the following detailed description when readin conjunction with the accompanying drawings, in which:

FIG. 1 is an equivalent circuit diagram of a conventional SAW filter;

FIG. 2 is a graph of a characteristic of the conventional SAW filtershown in FIG. 1;

FIG. 3 is a circuit diagram of a SAW filter according to the presentinvention;

FIG. 4 is a block diagram of the basic structure of a filter circuitusing a resonator;

FIGS. 5A, 5B and 5C are diagrams showing a one-terminal-pair SAWresonator;

FIGS. 6A and 6B are diagrams showing frequency characteristics ofimpedance and admittance of the one-terminal-pair SAW resonator;

FIGS. 7A to 7C are diagrams showing an immittance characteristic of aSAW resonator and a filter characteristic of the filter shown in FIG. 3using that SAW resonator;

FIGS. 8A to 8C are diagrams showing the characteristics of theconventional SAW filter shown in FIG. 1;

FIGS. 9A and 9B are diagrams showing effects obtained when an inductanceis connected in series to a resonator;

FIGS. 10A and 10B are diagrams showing effects obtained when none-terminal-pair resonators are connected in series;

FIGS. 11A and 11B are diagrams showing an aperture length dependence ona parallel-arm resonator;

FIGS. 12A to 12C are diagrams showing an aperture length dependence on aseries-arm resonator;

FIG. 13 is a circuit diagram of a SAW filter according to a firstembodiment of the present invention;

FIG. 14 is a diagram showing a band characteristic of the filter shownin FIG. 13;

FIGS. 15A and 15B are diagrams showing effects obtained when aninductance is added to a parallel-arm resonator;

FIG. 16 is a plan view of the structure of the SAW filter shown in FIG.13 with a lid removed therefrom;

FIG. 17 is a cross-sectional view taken along a line XVII—XVII shown inFIG. 16;

FIG. 18 is a diagram of a SAW filter according to a second embodiment ofthe present invention;

FIG. 19 is a diagram showing a band characteristic of the filter shownin FIG. 18;

FIGS. 20A and 20B are diagrams showing effects based on the ratio of theaperture length of the parallel-arm resonator to the aperture length ofthe series-arm resonator;

FIG. 21 is a diagram of a SAW filter according to a third embodiment ofthe present invention;

FIG. 22 is a diagram showing a band characteristic of the filter shownin FIG. 21;

FIG. 23 is a diagram of a SAW filter according to a fourth embodiment ofthe present invention;

FIG. 24 is a diagram showing a band characteristic of the filter shownin FIG. 23;

FIG. 25 is a circuit diagram of a SAW filter according to a fifthembodiment of the present invention;

FIG. 26 is a diagram showing a band characteristic of the filter shownin FIG. 25;

FIG. 27 is a circuit diagram of a SAW filter according to a sixthembodiment of the present invention;

FIG. 28 is a diagram showing a first one-terminal-pair SAW resonatorshown in FIG. 27;

FIG. 29 is a diagram showing a band characteristic of the filter shownin FIG. 27;

FIG. 30 is a diagram showing the influence of the reflector settingposition on the width of a ripple;

FIG. 31 is a plan view of the structure of the SAW filter shown in FIG.27 with a lid removed therefrom;

FIG. 32 is a diagram showing a variation of the first one-terminal-pairSAW resonator shown in FIG. 27;

FIG. 33 is a diagram showing another variation of the firstone-terminal-pair SAW resonator shown in FIG. 27;

FIG. 34 is a circuit diagram of a SAW filter according to a seventhembodiment of the present invention;

FIG. 35 is a diagram showing the relation between the film thickness ofthe electrode and the ripple occurrence position;

FIG. 36 is a diagram showing a state in which a ripple arising fromreflectors of a parallel-arm resonator has been dropped into ahigh-frequency attenuation pole;

FIGS. 37A, 37B and 37C are diagrams showing a film thickness' dependenceon the pass band characteristic of a resonator-type filter;

FIGS. 38A and 38B are diagrams showing the results of an experimentconcerning the film thickness' dependence on the insertion loss and theripple occurrence position;

FIG. 39 is a diagram of a first one-terminal-pair SAW resonatoraccording to an eighth embodiment of the present invention;

FIG. 40 is a diagram showing a band characteristic of the SAW filtershown in FIG. 39;

FIG. 41 is a diagram showing a variation of the first one-terminal-pairSAW resonator used in the eighth embodiment of the present invention;

FIG. 42 is a plan view of a structure which realizes inductors used inthe filter shown in FIG. 13;

FIG. 43 is a diagram of another structure which realizes inductors usedin the filter shown in FIG. 13;

FIG. 44 is a circuit diagram of a SAW filter according to an eleventhembodiment of the present invention;

FIG. 45 is a perspective view of the SAW filter shown in FIG. 44;

FIGS. 46A and 46B are diagrams showing an immittance characteristic of aSAW resonator in which the resonance frequency is higher than theanti-resonance frequency;

FIGS. 47A, 47B and 47C are diagrams showing variations in the bandcharacteristic of the ladder-type filter observed when the differencebetween the resonance frequency and the antiresonance frequencyincreases from zero;

FIGS. 48A and 48B are diagrams showing how to measure thecharacteristics of the SAW resonator;

FIG. 49 is a graph showing admittance and immittance characteristics ofSAW resonators in the series arm and the parallel arm;

FIG. 50 is a diagram showing the frequency dependence on the product ofbx;

FIG. 51 is a diagram showing an equivalent circuit in which a part ofthe circuit shown in FIG. 44 is expressed by means of L and C;

FIG. 52 is a diagram showing the relation between |bx_(max)| andΔf/f_(rs);

FIG. 53 is a diagram showing the relation between k² and τ;

FIG. 54 is a circuit diagram of a SAW filter according to a twelfthembodiment of the present invention;

FIG. 55 is a perspective view of the SAW filter shown in FIG. 54;

FIG. 56 is a diagram showing a filter characteristic of the SAWresonator shown in FIG. 53;

FIG. 57 is a diagram showing a characteristic obtained when anoutput-side admittance of the filter shown in FIG. 64 is reduced;

FIGS. 58A and 58B are circuit diagrams of unit sections;

FIGS. 59A, 59B and 59C are circuit diagrams showing multi-connections ofunit sections;

FIG. 60 is a diagram showing a connection of two four-terminal circuitsand an interface therebetween;

FIGS. 61A, 61B and 61C are circuit diagrams showing unit sectionconnecting ways;

FIG. 62 is a diagram showing how n unit sections are cascaded;

FIGS. 63A, 63B and 63C are circuit diagrams showing how ladder-typecircuits are configured using the unit sections;

FIG. 64 is a circuit diagram of a conventionalcomparative example of theSAW filter;

FIG. 65 is a circuit diagram of a SAW filter according to a thirteenthembodiment of the present invention;

FIG. 66 is a circuit diagram of a SAW filter according to a fourteenthembodiment of the present invention;

FIG. 67 is a diagram showing a SAW filter according to a fifteenthembodiment of the present invention;

FIG. 68 is a perspective view of the SAW filter shown in FIG. 57;

FIG. 69 is a diagram showing a filter characteristic of the filter shownin FIG. 68;

FIG. 70 is a circuit diagram of a ladder-type filter in which SAWresonators having different resonance frequencies are respectivelyprovided in the parallel and series arms;

FIGS. 71A and 71B are diagrams showing a frequency characteristic of theadmittance of the parallel-arm resonator and a frequency characteristicof the impedance of the series-arm resonator;

FIG. 72 is a circuit diagram of a wave filter according to a sixteenthembodiment of the present invention;

FIG. 73 is a Smith's chart of the wave filter shown in FIG. 72;

FIG. 74 is a circuit diagram of a wave filter according to a seventeenthembodiment of the present invention;

FIG. 75 is a Smith's chart of the wave filter shown in FIG. 74;

FIG. 76 is a circuit diagram of a wave filter according to an eighteenthembodiment of the present invention;

FIG. 77 is a Smith's chart of the wave filter shown in FIG. 76;

FIG. 78 is a circuit diagram of a wave filter according to a nineteenthembodiment of the present invention; and

FIG. 79 is a Smith's chart of the wave filter shown in FIG. 78.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 3 shows an overview of a SAW filter 20 according to the presentinvention. The SAW filter 20 comprises a first SAW resonator 21 having apair of terminals, a parallel arm 22, a second SAW resonator 23 having apair of terminals, a series arm 24, and an inductor 25. The firstresonator 21 connected to the parallel arm 22 has a predeterminedresonance frequency f_(rp). The second resonator 21 connected to theseries arm 24 has a predetermined resonance frequency f_(rs)approximately equal to an antiresonance frequency f_(ap) of the firstresonator 21. The inductor 25 is connected in series to the firstresonator 21, and provided in the parallel arm 22.

The principle of the SAW filter 20 will now be described. Use of imageparameters is convenient to verify whether or not a resonance circuithas a filter characteristic. The details of image parameters aredescribed in the following document: Yanagisawa et al., “Theory andDesign of Filters”, Sanpo Shuppan, Electronics Sensho, pp. 192-pp. 203,1974.

First of all, a basic ladder-type circuit having a filter characteristicwill be described with reference to FIG. 4. Two black boxes 30 and 31shown in FIG. 4 are respectively SAW resonators. For the sake ofsimplicity, it will now be assumed that the SAW resonators 30 and 31 arerespectively reactance circuits having no resistance, and that theimpedance Z of the resonator 30 provided in the series arm is equal tojx, and the admittance Y of the resonator 31 provided in the parallelarm is equal to jb.

According to the image parameter method, an image transfer quantity γ (acomplex number) defined in the following equation has the importantmeaning: $\begin{matrix}{{\exp(\gamma)} = \sqrt{V_{1} \cdot {I_{p}/V_{2}} \cdot I_{2}}} & (1)\end{matrix}$where V₁ and I₁ denote an input voltage and an input current,respectively, and V₂ and I₂ denote an output voltage and an outputcurrent, respectively. The equation (1) can be rewritten as follows:$\begin{matrix}\begin{matrix}{{\tan\quad{h(\gamma)}} = {\tanh\left( {\alpha + {j\beta}} \right)}} \\{= \sqrt{\left( {B \cdot C} \right)/\left( {A \cdot D} \right)}}\end{matrix} & (2)\end{matrix}$where A, B, C and D denote parameters of an F matrix showing the wholecircuit shown in FIG. 4. When the value expressed by the equation (2) isan imaginary number, the two-terminal-pair circuit shown in FIG. 4 has apass band characteristic. With the above value being a real number, thecircuit shown in FIG. 4 has an attenuation characteristic. The ABCDparameters can be rewritten using the above-mentioned x and b:A=1B=jxC=jbD=1−bx   (3).Hence, the following equation (4) can be obtained from the equation (2)using the above ABCD parameters: $\begin{matrix}{{\tan\quad{h(\gamma)}} = {\sqrt{{bx}/\left( {{bx} - 1} \right)}.}} & (4)\end{matrix}$When 0<bx<1, that is, when b and x have the same sign and are smallvalues, the entire circuit shown in FIG. 4 has a pass bandcharacteristic. When bx<0 or bx>1, that is, when the b and x havedifferent signs or the product of bx is a large value, the circuit shownin FIG. 4 has an attenuation characteristic.

In order to qualitatively understand the frequency characteristics of band x, the impedance and admittance of the SAW resonators will not beconsidered.

As shown in FIG. 5A, a SAW resonator having pair of terminals comprisesan interdigital electrode 40 (see “Nikkel Electronics”, November 29,pp.76-pp.98, 1976). A reference number 41 indicates a pair ofelectrodes, 42 indicates an aperture length (crossing width), and 43indicates an interdigital electrode period. When the resistance of theinterdigital electrode 40 is neglected, the SAW resonator shown in FIG.5A has an equivalent circuit 45 shown in FIG. 8B, in which C₀ denotesthe electrostatic capacitance of the interdigital electrode 40, C₁ andL₁ denote equivalent constants. Hereinafter, the equivalent circuit 45is depicted by symbol 46 shown in FIG. 5C.

FIGS. 6A and 6B qualitatively show an impedance vs. frequencycharacteristic (A) of the equivalent circuit shown in FIG. 5B, and anadmittance vs. frequency characteristic (B) thereof. The characteristicsshown in FIGS. 6A and 6B are double resonance characteristics in whichtwo resonance frequencies f_(r) and f_(a) exist. It will be noted that aresonator having a crystal has a double resonance characteristic. Whenthe resonators respectively having a double resonance characteristic arearranged in the series and parallel arms, respectively, and anantiresonace frequency f_(ap) of the parallel arm is made approximatelyequal to a resonance frequency f_(rs) of the series arm, a circuit canbe configured which has a band-pass-type filter characteristic havingthe center frequencies f_(ap) and f_(rs). This is because, as shown inan immittance vs. frequency characteristic shown in FIG. 7A, therelation 0<bx<1 is satisfied in a frequency range around the centerfrequency f_(ap)≈f_(rs) and that frequency range is a pass band, whilethe relation bx>1 is satisifed in a frequency range slightly away fromthe center frequency and the relation bx<0 is satisfied in a frequencyrange far away from the center frequency, the latter two frequencyranges serving as attenuation bands. Hence, the SAW filter shown in FIG.4 has a qualitative filter charateristic 47 shown in FIG. 7B.

A description will now be given of the factors that determine the bandwidth in the resonator-type SAW filters. As is seen from FIGS. 7A and7B, the band width is mainly dependent on the difference between theresonance frequency f_(r) and the antiresonance frequency f_(a) of eachof the two resonators. The band width increases as the above differenceincreases, while the band width decreases as the difference decreases.The resonance frequency f_(r) and the antiresonance frequency f_(a) canbe determined using the following equations, using the equivalentcircuit constants shown in FIG. 5B: $\begin{matrix}{f_{r} = {1/\left\lbrack {{2 \cdot \pi}\sqrt{\left( {C_{1} \times L_{1}} \right)}} \right\rbrack}} & (5) \\{f_{a} = {f_{r} \cdot \sqrt{\left( {1 + {1/\tau}} \right)}}} & (6) \\{\tau = {C_{0}/C_{1}}} & (7)\end{matrix}$where τ denotes the capacitance ratio. The ratio of the pass band to thecenter frequency (Δf/f_(o)) is mainly dependent on the differencebetween f_(r) and f_(a), and is therefore expressed in the followingexpression, using the equations (6) and (7):Δf/f_(o)=2(f_(a)−f_(r))/(f_(a)+f_(r))=2/(4τ+1)   (8).

It can be seen from the equation (8) that the capacitance ratio τ is themain factor which determines the ratio of the pass band to the centerfrequency. However, as set forth in Japanese Laid-Open PatentPublication No. 52-19044, the capacitance ratio is much dependent on thetype of substrate material used for the interdigital electrode. Forexample, an ST-cut crystal having a small electromechanical couplingcoefficient has a capacitance ratio τ equal to or greater than 1300,while a 36° Y-cut X-propagation LiTaO₃ substrate having a largeelectromechanical coupling coefficient has a capacitance ratio τ ofapproximately 15. The ratio of the pass band to the center frequency is0.04% for ST-cut crystal, and 3.3% for the 36° Y-cut X-propagationLiTaO₃ substrate. Hence, the band width is much dependent on thesubstrate material.

The band width decreases as the equivalent parallel capacitance C_(OB)increases in order to improve the side lobe suppression factor accordingto Japanese Laid-Open Patent Publication No. 52-19044.

The above phenomenon will now be described with reference to FIGS. 8A,8B and 8C. As is seen from the previous description of the principle ofthe present invention, as the admittance value increases while f_(r) andf_(a) of the parallel resonator (see, FIG. 8C) are kept constant, theproduct of bx has a negative sign and increases, as shown in FIG. 8A.However, the bx product increases around the center frequency, and hencethe range of bx>1 increases. Hence, the pass band in which the relation0<bx<1 stands is narrowed, and a sufficient pass band cannot beobtained. This phenomenon is indicated by arrows in FIG. 8B.

The following two conditions must be satisfied in order to eliminate theabove disadvantages. The first condition is to increase the differencebetween the resonance frequency f_(r) and the antiresonance frequencyf_(a) in at least one of the resonators provided in the series andparallel arms (see FIG. 8C). The second condition is to increase eitherthe impedance or admittance of the above-mentioned one of theresonators. As the impedance or admittance increases, the side lobeattenuation quantity increases. When the above two conditions awesatisfied, the side lobe attenuation quantity can be improved while thepass band is improved or prevented from being narrowed.

Regarding the first condition, it is effective to provide an inductor Lconnected in series to a SAW resonator having a pair of terminals inorder to increase the difference between f_(r) and f_(a). FIGS. 9A and9B respectively show an impedance vs. frequency characteristic of a SAWfilter in which an inductor having an inductance of 8 nH is connected toa resonator, and an admittance vs. frequency characteristic thereof. Theparameters of the equivalent circuits of the SAW resonators used forobtaining the characteristics are illustrated in FIGS. 9A and 9B.

FIG. 9A shows an impedance characteristic curve 50 obtained before theinductor L is connected to the resonator, and an impedancecharacteristic curve 51 obtained after the inductor is connectedthereto. FIG. 9B shows an admittance characteristic curve 52 obtainedbefore the inductor L is connected to the resonator, and an admittancecharacteristic curve 53 obtained after the inductor L is connectedthereto.

It can be seen from FIG. 9A that the inductance L increases the distancebetween the resonance frequency f_(r) and the antiresonance frequencyf_(a). In the graph of FIG. 9A, the distance is increased byapproximately 30 MHz. This is because, as shown in FIG. 9A, theinductance L functions to shift the impedance characteristic curve ofthe original resonator upwards to the plus side by ωL, and hence theresonance frequency f_(r) changes to f_(r)′. In this case, theantiresonance frequency f_(a) has little variation. The admittance,which is the reciprocal of the impedance, changes, as shown in FIG. 9B.In this case, the resonance frequency f_(r) changes to f_(r)′.

Regarding the aforementioned second condition, the admittance valueincreases due to the inductance L, as shown in FIG. 9B. However, asshown in FIG. 9A, the impedance value decreases in frequencies outsideof the pass band. Hence, if the inductance L is added to the resonatorprovided in the series arm, it is necessary to provide an additionalmeans for increasing the impedance value. The above additional means is,for example, an arrangement in which a plurality of identical SAWresonators are connected in series to each other (cascaded).

FIGS. 10A and 10B show an impedance characteristic curve 56 of aresonance arrangement in which n identical SAW resonators, each having apair of terminals, are cascaded. As shown in FIGS. 10A and 10B, theimpedance value of the resonance arrangement having the n cascadedresonators is n times that of the single resonator. The resonancefrequency of the resonator with the inductor L connected thereto isf_(r)″. That is, the difference between f_(r)″ and f_(a) of theresonance arrangement with the inductor L connected thereto is slightlysmaller than the difference between f_(r)′ and f_(a) of a singleresonator with the inductor L connected thereto. However, the differencebetween f_(r)″ and f_(a) of the resonance arrangement with the inductorL connected thereto is larger than that without the inductor L. It ispossible to further increase the difference between the resonancefrequency and the antiresonance frequency by using a larger inductanceL.

In order to increase the band width, it is also possible to select theantiresonance frequency f_(ap) of the parallel arm resonator and theresonance frequency f_(rs) of the series arm resonator so thatf_(rs)>f_(ap). In this case, the condition bx<0 occurs around the centerfrequency, and hence the aforementioned pass band condition is notsatisfied. Hence, there is a possibility that an insertion loss and aripple may increase. However, by controlling Δf=f_(vs)−f_(ap), it ispossible to substantially suppress the increase in the insertion lossand the ripple and to expand the increase in the pass band.

A description will now be given of embodiments of the present invention.The embodiments which will be described are based on a simulation.Hence, this simulation will be described first, as well as the resultsof comparisons between the experimental results and the simulation inorder to show the validity of the simulation.

The equivalent circuit shown in FIG. 5B easily simulates thecharacteristic of the SAW resonator having a pair of terminals, whilethat equivalent circuit is not suitable for simulating, with highaccuracy, variations in the number of figure pairs, the aperture lengthand the electrode thickness, and the effects of a reflector. With theabove in mind, the inventors have proposed an improved simulation whichuses a Smith's equivalent circuit model and expands a transfer matrix toanalyze the SAW resonators (see O. Ikata et al., “1990 ULTRASONICSYMPOSIUM Proceedings, vol. 1, pp.83-pp.86, 1990; the disclosure ofwhich is hereby incorporated by reference).

FIG. 11A is a graph showing the results of the simulation (calculation)for an arrangement in which a SAW resonator having a pair of terminalsis disposed in the parallel arm. FIG. 11B is a graph showing the resultsof the experiment on an arrangement in which a one-terminal-pair SAWresonator including an interdigital electrode made of Al-2% Cu andhaving a film thickness of 1600 Å is disposed in a parallel arm, andbonding wires (L=1.5 nH) having a length of 3 mm are connected to theinterdigital electrode. It can be seen from FIGS. 11A and 11B that thecalculation values match the experiment values with respect tovariations in the resonance points (f_(r1), f_(r2), f_(r3)) as well asthe attenuation quantities observed around the resonance points fordifferent aperture lengths (a=60, 150, 300 μm).

FIG. 12A is a graph showing the results of the simulation for anarrangement in which a SAW resonator having a pair of terminals isdisposed in the series arm (see, FIG. 12C). The bonding pads used in theexperiment which will be described later were slightly large, and thesimulation was carried out taking into account a stray capacitance 0.5pF of the bonding pads. FIG. 12B is a graph showing the results of theexperiment on an arrangement in which a SAW resonator having a pair ofterminals is disposed in the series arm. It can be seen from FIGS. 12A,12B and 12C that the antiresonance frequencies f_(a1), f_(a2) and f_(a3)do not depend on the aperture length and that the simulation resultsmatch the experimental results regarding variations in the attenuationquantity around the resonance frequencies.

Hence, it will be apparent from the above that the results of asimulation of the filter with the combination of the resonators disposedin the parallel and series arms match the results of the experiment. Theembodiments described below are based on the result of simulations.

FIG. 13 shows a SAW filter 60 according to a first embodiment of thepresent invention. In Japan, an automobile and portable telephone systemhas a specification in which the ±8.5 MHz range about a center frequencyof 933.5 MHz is a transmission band for mobile telephones and the ±8.5MHz range about a center frequency of 878.5 MHz separated from 933.5 MHzby −55 MHz is a receptionrejection band. The SAW filter 60 according tothe first embodiment of the present invention is designed to be suitablefor transmission filters of mobile telephones.

As shown in FIG. 13, two one-terminal-pair SAW resonators R2 and R4 arearranged in a series arm 61, and three one-terminal-pair SAW resonatorsR1, R3 and R5 are respectively arranged in parallel arms 62, 63 and 64.Inductors L1, L2 and L3 are provided in the parallel arms 62, 63 and 64,and are connected in series to the resonators R1, R3 and R5,respectively. Each of the resonators R1-R5 has the interdigitalelectrode structure shown in FIG. 5A. The number of finger pairs is 100,and the aperture length is 80 μm. The electrodes are made of Al-2% Cu,and are 3000 Å thick. The resonance frequencies of the resonators R1, R3and R5 respectively provided in the parallel arms 62, 63 and 64 are 912MHz, and the antiresonance frequencies thereof are 934 MHz. Theresonance frequencies of the resonators R2 and R4 respectively providedin the series arm 61 are 934 MHz, and the antiresonance frequenciesthereof are 962 MHz. The inductors L1, L2 and L3 respectively have aninductance L of 4 nH.

The SAW filter 60 having the above structure has a band characteristicindicated by a curve 65 shown in FIG. 14. Characteristic curves 66 and67 in FIG. 14 are respectively obtained when the inductance L is equalto 2 nH and 6 nH.

A curve 70 shown in FIG. 15A illustrates the inductance' dependence onthe band width obtained on the basis of the graphs of FIG. 14. The bandwidth is defined as the frequency width between the points on the curvewhere the insertion loss is 3 dB greater than the minimum value.

A curve 71 shown in FIG. 15B illustrates a side lobe suppression factor'dependence on the inductance obtained on the basis of the graphs of FIG.14. It can be seen from FIG. 14 that a sufficient suppression factor isnot obtained at a frequency which is 55 MHz lower than the centerfrequency when the inductance L is too large. With the above in mind, aninductance L of 4 nH is selected. The value of the inductance L issuitable selected in accordance with the specification of filters.

A curve 68 in FIG. 14 shows a band characteristic of a configuration inwhich L1=L2=L3=0 in FIG. 13. It can be seen from comparison between theband characteristic (curve 65) of the first embodiment and that (curve68) of the conventional filter that the filter 60 according to the firstembodiment has a large pass band width (arrow 75), a large side lobesuppression factor (arrows 76), and a low insertion loss (arrow 77).

FIGS. 16 and 17 show a SAW filter device 80 which functions as the SAWfilter 60 shown in FIG. 13. The SAW filter device 80 comprises a ceramicpackage 81, a filter chip 82, and a lid 83 serving as the ground. Theceramic package 81 is made of alumina ceramics, and has dimensions of5.5 mm (length)×4 mm (width)×1.5 mm (height). Electrode terminals 84⁻¹-84 ⁻⁶ made of Au are formed on the ceramic package 81. The filterchip 82 is made of LiTaO₃, and has dimensions of 2 mm (length)×1.55 mm(width)×0.5 mm (thickness).

Resonators R1-R5 are arranged on the filter chip 82 so that each of theresonators R1-R5 does not own propagation paths in common with otherresonators. Each of the resonators R1-R5 has an interdigital electrodemade of Al-2% Cu in which the number of finger pairs is 100, theaperture length is 80 μm, and the film thickness is 3000 Å.

Further, two signal line terminals 85 ⁻¹ and 85 ⁻² for bonding and threeground terminals 85 ⁻³, 85 ⁻⁴ and 85 ⁻⁵ for bonding are formed on thesurface of the filter chip 82. Reference numbers 86 ⁻¹-86 ⁻⁵ indicatebonding wires made of Al or Au. The bonding wires 86 ⁻¹-86 ⁻⁵, eachhaving a diameter of 25 μmø, connects the terminals 84 ⁻¹-84 ⁻⁵ and theterminals 85 ⁻¹-85 ⁻⁵. The bonding wires 86 ⁻¹ and 86 ⁻² respectivelyform parts; of the series arms 61a and 61b. The wire 86 ⁻³ is connectedbetween the ground electrode terminals 84 ⁻³ and 85 ⁻³, and the wire 86⁻⁴ is connected between the ground electrode terminal 84 ⁻⁴ and 85 ⁻⁴.The wire 86 ⁻⁵ is connected between the ground electrode terminals 84 ⁻⁵and 85 ⁻⁵. The wires 86 ⁻³-86 ⁻⁵ are long and, for example, 2.0 mm long.

According to the theory of high frequencies, a fine, long wire has aninductance component. According to the theoretical equation of a ribboninductor located in a space (see Kuraishi, “Exercise Microwave Circuit”,Tokyo Denki Daigaku Shuppan-Kyoku, pp. 199), the inductances of thewires 86 ⁻³, 86 ⁻⁴ and 86 ⁻⁵ are approximately equal to 1 nH. It If thehigh attenuation and wide pass band are needed, it is insufficient toobtain an inductance of 4 nH by means of only the wires. As will bedescribed later, inductors are formed on the ceramic package 81 and thefilter chip 82. In this manner, the inductors L1, L2 and L3 are formed.

A description will now be given of a SAW filter according to a secondembodiment of the present invention. FIG. 18 shows a SAW filter 90according to the second embodiment of the present invention. In FIG. 18,parts that are the same as parts shown in the previously describedfigures are given the same reference numbers. The resonator R2 in theseries arm 61 has an aperture length As of 80 μm. A resonator and theinductor L1 connected in series to each other are provided in theparallel arm 62. The resonator R1A has an aperture length Ap of 120 μm.The aperture length Ap is larger than the aperture length As, being 1.5times the aperture length As. The numbers Np and Ns of finger pairs ofthe resonators R2 and R1A are 100.

The filter 90 shown in FIG. 19 has a band characteristic indicated by acurve 91 shown in FIG. 19. It can be seen from comparison between thecurve 91 and the characteristic curve 65 of the filter 60 that thefilter 90 has an improved side lobe suppression factor without a changein the pass band width.

FIGS. 20A and 20B show a band characteristic' dependence on the aperturelength in the filter shown in FIG. 18. More particularly, FIG. 20A showsa curve 92 indicating the dependence on the aperture length with aninductance L of 4 nH connected to the resonator, and a curve 93indicating the dependence on the aperture length without any inductance.The horizontal axis of FIG. 20A denotes the ratio Ap/As, and thevertical axis thereof denotes the side lobe suppression factor (dB).FIG. 20B shows a pass band width s the ratio Ap/As characteristic. Acurve 95 indicates the dependence on inductance with an inductance L of4 nH connected to the resonator, and a curve 96 indicates the dependenceon inductance without any inductance.

The following can be seen from FIGS. 20A and 20B. First, the side lobesuppression factor increases when making the aperture length Ap of theresonator R1A in the parallel arm 62 larger than the aperture length Asof the resonator R2 in the series arm 61. Second, the effect of theaperture length Ap of the resonator R1A is increased withoutdeterioration of the pass band width by providing the inductor L1 in theparallel arm 62. It can be seen from the above that the filter 90 has animproved side lobe suppression factor while the pass band width is notnarrowed, as compared to the filter 60.

A description will now be given of a third embodiment of the presentinvention with reference to FIG. 21, in which parts that are the same asparts shown in the previously described figures are given the samereference numbers. A SAW filter 100 shown in FIG. 21 comprises aresonator R1B provided in the parallel arm 62, and the resonator R2provided in the series arm 61. The number Ns of finger pairs of theresonator R2 is 100. The inductor L1 is connected in series of theresonator R1B. The number Np of finger pairs of the resonator R1B is150, and is 1.5 times the number Ns of finger pairs. The aperturelengths As and Ap of the resonators R2 and R1A are 80 μm.

The filter 100 shown in FIG. 21 has a band characteristic indicated by acurve 101 shown in FIG. 22. It can be seen from comparison between theband characteristic curve 65 of the filter 60 and the characteristiccurve 101 of the filter 100 that the filter 100 has an improved sidelobe suppression factor indicated by arrows 102 without reducing thepass band width. It can also be seen from comparison between the bandcharacteristic curve 91 of the filter 90 and the characteristic curve101 that the insertion loss of the filter 100 is less than that of thefilter 90. Hence, the filter 100 has an improved side lobe suppressionfactor while the pass band width is reduced, and has an insertion losssmaller than that of the filter 90.

A description will now be given of a fourth embodiment of the presentinvention with reference to FIG. 23, in which parts that are the same asparts shown in the previously described figures are given the samereference numbers. A filter 110 according to the fourth embodiment isintended to increase the difference between the resonance frequencyf_(r) and the antiresonance frequency f_(a) of the resonator in theseries arm and to thereby improve the band characteristic. Two identicalresonators R2 are provided in the series arm 61, and two identicalresonators R4 are provided therein. An inductor Ls having an inductanceof 3 nH is connected in series to the resonators R2, and anotherinductor Ls having an inductance of 3 nH is connected in series to theresonators R4. The resonators R1, R3 and R5 are respectively provided inthe parallel arms 62, 63 and 64. The filter 110 has a bandcharacteristic indicated by a curve 111 shown in FIG. 24.

A description will now be given of the effects provided by adding oneinductor Ls and two resonators R2 and R4. When one inductor Ls and tworesonators R2 and R4 are omitted from the filter 110, the remainingcircuit configuration consists of five resonators R1, R2, R3, R4 and R5.The band characteristic of the remaining circuit configuration isindicated by a curve 68 (see FIG. 14). By adding one inductor Ls, thepass band width is increased, as indicated by arrows 112 and the sidelobe suppression factor is also increased, as indicated by arrows 113.Particularly, the pass band width is large at frequencies higher thanthe center frequency, and is increased by approximately 15 MHz. The bandcharacteristic with the inductor Ls added to the conventional filter 1is indicated by curve 114. In this case, a sufficient side lobesuppression factor is not obtained. Hence, two resonators R2 and R4 arefurther added to the conventional filter 1 with the inductor Ls addedthereto. As indicated by arrows 115, the side lobe suppression factor isimproved by approximately 5 dB without reducing the band characteristic,and a band characteristic curve 111 can be obtained. It can be seen fromcomparison between the curves 111 and 68 that the insertion loss is alsoimproved, as indicated by arrows 116. It is possible to use more thantwo resonators R2 and more than two resonators R4. Further, as indicatedby the two-dot chained line in FIG. 23, inductors can be provided in theparallel arms 62-64.

A description will now be given of a fifth embodiment of the presentinvention with reference to FIG. 25, in which parts that are the same asparts shown in the previously described figures are given the samereference numbers. A SAW filter 120 shown in FIG. 25 comprises fiveresonators R1-R5, and three inductors L1-L3. The inductor L1 in theparallel arm 62 has an inductance Lp1 of 4 nH, and the inductor L2 inthe parallel arm 63 has an inductance Lp2 of 5.5 nH. Further, theinductor L3 in the parallel arm 64 has an inductance Lp3 of 7 nH.

By making the inductors L1, L2 and L3 have different inductance values,the filter 120 has a band characteristic indicated by a curve 121 shownin FIG. 26. Let us compare the characteristic curve 121 with thecharacteristic curve 65 (FIG. 14) of the filter 60 shown in FIG. 13 inwhich all the inductance values are the same as each other. It can beseen from the above that the filter 120 has an improved side lobecharacteristic without reducing the pass band width, as compared to thefilter 60. The characteristic curve has an attenuation pole 123 locatedaround a frequency of 902 MHz, while the characteristic curve 121 hastwo attenuation poles 124 and 125 respectively located around 875 MHzand 892 MHz. A frequency band 126 between the poles 124 and 125functions as a blocking range 127.

A description will now be given of a sixth embodiment of the presentinvention with reference to FIG. 27, in which parts that are the same asparts shown in the previously described figures are given the samereference numbers. A SAW filter 130 shown in FIG. 27 comprises two SAWresonators R2 and R4 provided in the series arm 61, and three SAWresonators R1B, R3B and R5B respectively provided in the parallel arms63 and 64.

As shown in FIG. 28, the resonator R1B has an exciting interdigitalelectrode 131, and reflectors 132 and 133 respectively disposed on bothsides of the electrode 131. The reflectors 132 and 133 are positioned sothat β=0.4 in which β is obtained from the following equation:d=(n+β)·λwhere d is the distance between the center of the electrode 131 and eachof the reflectors 132 and 133, n is an arbitrary integer, β is a realnumber equal to or less than 1, and λ is the period of the interdigitalelectrode 131 corresponding to its resonance frequency.

The number of finger pairs of each of the reflectors 132 and 133 is 50.The resonators respectively equipped with the reflectors are indicatedby the symbol “*” shown in FIG. 27. The resonators R3B and R5Brespectively provided in the parallel arms 63 and 64 respectively havetwo reflectors in the same manner as the resonator R1B.

The filter 130 shown in FIG. 27 has a band characteristic indicated by acurve 134 shown in FIG. 29. As compared to the characteristic curve 85of the filter 80 (FIG. 13), the insertion loss in the filter 130 isimproved, as indicated by an arrow 135. A ripple r_(p) arises from thearrangement of the reflectors 132 and 133.

A description will now be given of the reason why the reflectors 132 and133 are arranged in the above-mentioned manner. The influence of theripple r_(p) observed when β is changed from 0 to 0.5 is illustrated bya curve 140 shown in FIG. 30. The smallest ripple width can be obtainedat a point 141 at which β is 0.4.

FIG. 31 shows a SAW filter device 150 functioning as the filter 130shown in FIG. 27. In FIG. 31, parts that are the same as parts shown inthe previously described figures are given the same reference numbers aspreviously. The filter device 150 comprises reflectors 132, 133, 151,152, 153 and 154.

Variations of the one-terminal-pair SAW resonators R1B, R3B and R5B willnow be described.

FIG. 32 shows a first variation R1Ba, which comprises interdigitalelectrodes 180 and respectively arranged on both sides of the excitinginterdigital electrode 131. Each of the interdigital electrodes 180 and181, which functions as a reflector, is an electrode in which theelectric load thereof is of a short-circuit type.

FIG. 33 shows a second variation R1Bb, which comprises strip array typeelectrodes 167 and 166 respectively arranged on both sides of theelectrode 131.

A description will now be given of a seventh embodiment of the presentinvention with reference to FIG. 34, in which parts that are the same asparts shown in the previously described figures are given the samereference numbers. A SAW filter 170 shown in FIG. 34 comprises two SAWresonators R2 and two resonators R4 respectively provided in the seriesarm 61, and three SAW resonators R1B, R3B and R5B respectively providedin the parallel arms 62, 63 and 64. Two inductors Ls are provided in theseries arm 61, as shown in FIG. 34.

The filter 170 is obtained by replacing the resonators R1, R3 and R5shown in FIG. 23 with the resonators R1B, R3B and R5B shown in FIG. 28.As has been described previously, the reflectors 132 and 133 shown inFIG. 28 are positioned so that the condition β=0.4 is satisfied. Thefilter 170 has a loss of the pass band smaller than that of the filter110 shown in FIG. 23, and a suppressed ripple.

A description will now be given of an eighth embodiment of the presentinvention, which is intended to eliminate the ripple r_(p) shown in FIG.29. First of all, a means for effectively eliminating the ripple r_(p)arising from the reflectors will be described.

The inventors simulated the relationship between the frequencies atwhich the ripple r_(p) is observed and the electrode thickness. In thesimulation, the effects resulting from increasing the film thickness ofthe electrode are replaced by increasing the ratio between the acousticimpedance (Z_(m)) obtained under the electrode and the acousticimpedance (Z_(o)) of the free surface. As described in theaforementioned Ikata document, an increase in the electrode thicknessincreases the weight thereof. Hence, it is possible to consider that anincrease in the electrode thickness is proportional to an increase in adiscontinuous quantity of the acoustic impedance. With the above inmind, the following equation was prepared:Q=Z_(o)/Z_(m)=V_(o)/V_(m)=1+k²/2+α(t)   (9)where V_(o) and V_(m) respectively denote sound velocities on the freesurface and under the electrode, k² is the electromechanical couplingcoefficient, and t is the film thickness of the electrode. Then α(t) waschanged as a parameter proportional to the film thickness t.

From the equation (9), the center frequency f_(o) of the filter iswritten as follows:f_(o)=2f_(o)′/(1+Q)   (10).The equation (10) is consistent with the well-known experimental resultin which, as the film thickness increases, the center frequencydecreases from the center frequency f_(o)′ obtained when there is nodiscontinuity of the acoustic impedance. The results of the simulationshow that, as α(t) increases, that is, the film thickness increases, thefrequency position at which the ripple r_(p) appears shifts toward thehigh-frequency range of the pass band, as indicated by an arrow 180shown in FIG. 35, and finally drops into the attenuation pole on thehigh-frequency side of the pass band. It will be noted that a rippler_(s) shown in FIG. 35 is caused by the reflectors of the resonatorsprovided in the series arm.

FIG. 36 shows an attenuation quantity vs. frequency characteristicobtained when α(t)=0.05. A ripple resulting from the reflectors of theresonators in the parallel arms is located in the attenuation pole onthe high-frequency side of the pass band. That is, there is no ripple inthe pass band. In addition, the graph of FIG. 36 shows that theinsertion loss is very small. In FIG. 36, the resonance frequencies ofthe resonators in the parallel and series arms are calibrated so thatthey are located at the frequency position which is 15 MHz higher thanthe original frequency position in order to obtain a center frequency of932 MHz, because the center frequency of the pass band decreasesaccording to the equation (10).

The inventors fabricated chips and measured the band characteristicthereof in order to study the relation to the actual film thickness.

FIGS. 37A, 37B and 37C respectively show band characteristic curves 185,186 and 187 for film thicknesses of 2000 Å, 3000 Å and 4000 Å. Inpractice, the center frequency is varied by changing the film thickness.The graphs of FIGS. 37A, 37B and 37C have been calibrated by changingthe period of the interdigital electrode.

A ripple r_(p) resulting from the resonators in the parallel arms issuperimposed on the characteristic curve 185 for a film thickness of2000 Å. As the film thickness increases, the ripple r_(p) shifts tohigher frequencies. The experimental results shown in FIGS. 37A, 37B and37C are consistent with the aforementioned results of the simulation.

However, an insertion loss arising from a bulk wave, which cannot becalculated by simulation, and a resistance loss appear as the filmthickness increases (see Ebata et al., “SURFACE ACOUSTIC WAVE RESONATORON LiTaO₃ SUBSTRATE AND ITS APPLICATION TO OSCILLATORS FOR USE IN VTR”,Journal of the Institute of Electronics and Communication Engineers ofJapan, vol. J66-C, No.1, pp.23-pp.30, 1988). Further, the correlationbetween the above insertion loss and the resistance loss is also a veryimportant factor.

FIG. 38A shows a curve 190 of the insertion loss resulting from the bulkwave, and a resistance loss curve 191. A curve 192 shows an experimentalcharacteristic curve. The insertion loss is approximately equal to theresistance loss when the film thickness is 2500 Å. Then, the total lossmainly resulting from the insertion loss starts to increase when thefilm thickness is approximately 3500 Å.

A curve 193 shown in FIG. 38B indicates the frequency position f_(rp) ofthe ripple r_(p) as a function of the identical film thickness of theexciting electrode 131 and the reflectors 132 and 133 shown in FIG. 28.It is concluded, based on the graphs in FIGS. 38A and 38B of FIG. 38,that the optimum film thickness that results in no ripple and littleinsertion loss is between 2600 Å and 4000 Å. The above optimum filmthickness can be normalized by the period λ_(p) (4.4 μm at 932 MHz seeFIG. 28) of the resonators in the parallel arm substantially determinedby the center frequency of the filter. The normalized optimum filmthickness is between 0.06 and 0.09.

The eighth embodiment of the present invention is based on the resultsof the above consideration by the inventors.

FIG. 39 shows a first one-terminal-pair SAW resonator 200 used in theSAW filter according to the eighth embodiment. The resonator 200comprises an exciting electrode 201, and two reflectors 202 and 203respectively located on both sides of the electrode 201. The electrode201 and the reflectors 202 and 203 are made of aluminum (Al) or amixture or alloy of Al and a few percentage of other metal by weight.The film thickness t₁ of each of the electrodes and the reflectors 202and 203 is equal to 0.06-0.09 times the electrode period λ_(p). A SAWfilter, in which the resonator 200 is applied to each of the resonatorsR1B, R3B and R5B shown in FIGS. 27 and FIG. 34, has a bandcharacteristic indicated by a curve 205 shown in FIG. 40. It can be seenfrom FIG. 40 that there is no ripple in the pass band. Use of an Alalloy improves the breakdown power performance, as compared to use ofAl, Cu or Ti can be mixed with Al.

FIG. 41 shows a variation 210 of the SAW resonator 200. The resonator210 shown in FIG. 41 comprises an exciting interdigital electrode 211,and two reflectors 212 and 213 respectively located on both sides of theelectrode 211. The electrode 211 and the reflectors 212 and 213 are madeof Au. The optimum film thickness of the electrode 211 and thereflectors 212 and 213 is determined, taking into account theabove-mentioned phenomenon caused due to the influence of an increase inthe weights of the electrode 211 and the reflectors 212 and 213. Sincethe ratio of the density of Al to that of Au is 2.7/18.9, equal to0.143, the optimum film thickness t₂ is determined by multiplying theoptimum film thickness t₁ by 0.143, and is equal to 0.0086-0.013 timesthe electrode period λ_(p). A SAW filter obtained by applying theresonator 210 to each of the resonators R1B, R3B and R5B has a bandcharacteristic similar to the characteristic shown in FIG. 40, and doesnot have any ripple in the pass band.

A description will now be given of the structure of the inductors L1, L2and L3 shown in FIG. 13 according to a ninth embodiment of the presentinvention, with reference to FIG. 42, in which parts that are the sameas parts shown in FIG. 16 are given the same reference numbers. As shownin FIG. 42, zigzag microstrip lines 220 and 221 are formed on theceramic package 81 and are connected to the terminals 84 ⁻³ and 84 ⁻⁵.Ends of the microstrip lines 220 and 221 are connected to the ground.The pattern width of each of the microstrip lines 220 and 221 is 100 μm,and the distance between the microstrip lines 220 and 221 and the groundis 0.5 mm. When the dielectric constant of the ceramic package 81 isequal to 9, the inductance values of the microstrip lines 220 and 221are equal to 2 nH.

A description will now be given, with reference to FIG. 43, of a tenthembodiment of the present invention which is another structure of theinductors L1, L2 and L3. In FIG. 43, parts that are the same as partsshown in FIG. 16 are given the same reference numbers as previously. Twozigzag microstrip lines 230 and 231 respectively connected to theresonators R1 and R2 are formed on the filter chip 82. Terminals 85 ⁻³and 85 ⁻⁵ are connected to ends of the microstrip lines 230 and 231.Each of the microstrip lines 230 and 231 is 3000 Å thick, 60 μm wide and2 mm in length. When the dielectric constant of the filter chip (LiTaO₃)82 is equal to 44, the inductance of the microstrip lines 230 and 231are equal to 2.2 nH.

It is possible to form inductors by suitably combining the bonding wire86 ⁻³, the microstrip line 220 on the ceramic package 81 and themicrostrip line 230 on the filter chip 82.

A description will now be given, with reference to FIG. 44, of a SAWfilter 240 according to an eleventh embodiment of the present invention.The eleventh embodiment of the present invention is configured asfollows. First, the resonance frequency f_(rs) of the resonators in theseries arm is made higher than the antiresonance frequency f_(ap) of theresonators in the parallel arms in order to increase the pass bandwidth. Second, Δf≡f_(rs)−f_(ap) is selected so that the pass band doesnot have an extremely large loss.

The previously described embodiments of the present invention requirethat f_(ap)=f_(rs). However, as long as this condition is maintained,the pass band cannot be increased. In order to increase the pass band,the present inventors considered a condition f_(ap)<f_(rs), as shown inFIGS. 46A and 46B. It is apparent from FIGS. 46A and 46B that bx<0within a range f_(ap)<f<f_(rs) and hence this frequency range is changedto an attenuation band according to the aforementioned theory. However,in practice, the product bx can be maintained at a very small value bylimiting Δf=(f_(rs)−f_(ap)), and the above frequency range canpractically function as a pass band without any substantial attenuation.

FIGS. 47A, 47B and 47C show band characteristics of a ladder-type filterobtained when the Δf=(f_(rs)−f_(ap)) increases from zero. The filterused in the experiment has a piezo-electric substrate made of LiTaO₃having an electromechanical coupling coefficient of 0.05, and an Alinterdigital electrode having a film thickness of 3000 Å. The structureof the electrode is one of two basic units connected so as to form aladder-type structure, as shown in FIG. 44. Each of the basic unitscomprises a first resonator in the parallel arm and a second resonatorin the series arm. In order to form the input and output parts of thefilter in symmetry to each other, a third resonator is provided inanother parallel arm of the final stage. A plurality of basic units arecascaded so as to form a ladder-type structure in order to increase theside lobe suppression factor to a practical value.

However, the insertion loss increases as the number of basic units to becascaded increases. Hence, it is preferable to determine the number ofbasic units to be cascaded, taking into account an actual filterspecification. The filter being considered is intended to realize a lossequal to or less than 2 dB and a side lobe suppression factor equal toor higher than 20 dB. The interdigital electrode of each of theresonators in the parallel and series arms is designed to have anaperture length of 180 μm and 50 finger pairs. The ratio P=(Cop/Cos)obtained when Cop and Cos are electrostatic capacitances of parallel-armand series-arm, respectively, is 1 because the electrodes of all theresonators have identical specifications.

FIG. 47A shows a band characteristic when Δf=0. FIG. 47B shows a bandcharacteristic when Δf=10 MHz. The band characteristic shown in FIG. 47Bis improved so that the pass band width (in which a loss equal to orless than 2.5 dB is ensured) is increased to 40 MHz, while the bandcharacteristic shown in FIG. 47A has a pass band width of 22 MHz. It canbe seen from FIGS. 47A and 47B that the pass band width is improvedparticularly for low frequencies. Further, the band characteristic shownin FIG. 47B has an improved side lobe suppression factor. Moreparticularly, the side lobe suppression factor is improved to 20 dB from19 dB.

There is a limit regarding improvement due to increase in Δf. FIG. 47Cshows a band characteristic when Δf=19 MHz. The pass band width slightlydeteriorates at high frequencies, and this deterioration isapproximately equal to 2.5 dB, which will increase the ripple in thepass band. In FIG. 47C, a ripple amounting to approximately 1.0 dB,which is the allowable ripple limit, is observed. When Δf is furtherincreased, the insertion loss and the in-band ripple increase. Hence, anincrease of Δf=19 MHz is the limit.

The product bx obtained when Δf=19 MHz was examined. In the experiment,a SAW resonator provided in a parallel arm shown in FIG. 44 and a SAWresonator provided in a series arm shown therein were separatelyfabricated. The admittance of the resonator in the parallel arm wasmeasured by means of a circuit configuration shown in FIG. 48A, and theimpedance of the resonator in the series arm was measured by means of acircuit configuration shown in FIG. 48B. The measurement of admittanceand impedance was carried out by measuring S21 by means of a networkanalyzer. The measured values of S21 were inserted into equations shownin FIGS. 48A and 48B, and the impedance Z_(p) and the admittance Y_(p)were calculated.

A frequency characteristic shown in FIG. 49 was obtained, which showsthe imaginary part of the admittance or impedance, that is, the value ofb or x. The frequency dependence of the product bx is as shown in FIG.50. It can be seen from FIG. 50 that the product bx is negative and is asmall value within f_(ap)<f<f_(rs). The maximum absolute value|bx_(max)| of the product bx is given when:$f = \sqrt{f_{ap} \cdot f_{rs}}$and was equal to 0.06 for the embodiment being considered. That is, whenvalue |bx_(max)| is equal to or smaller than 0.06, and deterioration ofthe insertion loss can be reduced and the in-band ripple can besuppressed to 1 dB or less. If Δf>19 MHz, the value of |bx_(max)|increases, and both the insertion loss and the in-band ripple willincrease to 1 dB or greater. This value is not practical. As a result,the value of |bx_(max)| is a an upper-limit indicator of characteristicdeterioration, and determines the allowable value of Δf.

The above consideration will be generalized. FIG. 51 is an equivalentcircuit diagram of a ladder-type filter obtained by approximating theSAW resonators by the double resonance circuits of LC. The impedanceZ_(s) of the SAW resonator in the series arm and the admittance Y_(p) ofthe SAW resonator in the parallel arm are expressed as follows:$\begin{matrix}\begin{matrix}{Z_{s} = {jx}} \\{= {\left\lbrack {- {j\left( {\omega_{rs}^{2} - \omega^{2}} \right)}} \right\rbrack/\left\lbrack {C_{os}\left( {\omega_{as}^{2} - \omega^{2}} \right)} \right\rbrack}}\end{matrix} & (11) \\{\Upsilon_{p} = {jb}} & (12) \\{\quad{\text{[} = {{\left\lbrack {{jC}_{op}\left( {\omega_{ap}^{2} - \omega^{2}} \right)} \right\rbrack/\left( {\omega_{rp}^{2} - \omega^{2}} \right)}\text{]}}}} & \quad \\{\quad{= {\left\lbrack {{- j}\quad{C_{op}\left( {\omega_{ap}^{2} - \omega^{2}} \right)}} \right\rbrack/\left( {\omega_{as}^{2} - \omega^{2}} \right)}}} & \quad\end{matrix}$where ω_(rs), ω_(as), ω_(rp), ω_(ap) are respectively the resonance andantiresonance frequencies of the series-arm resonator and the resonanceand antiresonance frequencies of the parallel-arm resonator, and τ isthe capacitance ratio (inherent in the substrate). The above resonanceand antiresonance frequencies as well as the capacitance ratio arewritten as follows:$\omega_{rs} = {{2{\pi f}_{rs}} = {1/\sqrt{C_{1s}L_{1s}\lambda}}}$$\omega_{as} = {{2{\pi f}_{as}} = {\omega_{\tau s}\sqrt{1 + {1/\tau}}}}$$\omega_{rp} = {{2{\pi f}_{rp}} = {1/\sqrt{C_{1p}L_{1p}}}}$$\omega_{ap} = {{2{\pi f}_{ap}} = {\omega_{rp}\sqrt{1 + {1/\tau}}}}$τ = C_(0s)/C_(1s) = C_(0p)/C_(1p).

The product bx is calculated from the equations (11) and (12) asfollows:bx=−[C_(0p)·(ω_(ap) ²−ω²)·(ω_(rs)−ω²)]/[C_(0s)·(ω_(rp) ²−ω²)·(ω_(as)²−ω²)]  (13)The angular frequency ω which makes the product bx have a pole isobtained from δ(bx)/δω=0, and is expressed as follows: $\begin{matrix}{= {\sqrt{\omega_{ap} \cdot \omega_{rs}}.}} & (14)\end{matrix}$The value obtained by inserting the above into the equation (13) is themaximum value of the product bx in the pass band. That is,bx_(max)=−[C_(0p)·(1+1/τ)]/[C_(0s)·{1+1/(τ·Δω/ω_(rs)}⁻²]  (15)whereΔω=ω_(rs)−ω_(ap)=2π·Δf   (16)

FIG. 52 shows a relation between bx_(max) and Δf/f_(rs) obtained byplotting the equation (15) as a parameter P=C_(0p)/C_(0s). The hatchedarea shown in FIG. 52 corresponds to the condition such that theallowable value of the product bx is equal to or smaller than 0.06obtained by the experiment. Hence, the allowable value α of Δf/f_(rs)dependent on P=C_(0p)/C_(0s) can be determined, and is written asfollows, by inserting |bx_(max)|=0.06 into the equation (15):$\begin{matrix}{\alpha = {1/{\left\lbrack {\sqrt{{P\left( {\tau^{2} + \tau} \right)}/0.06} - \tau} \right\rbrack.}}} & (17)\end{matrix}$

The capacitance ratio τ depends on the substrate material, and isapproximately 15 for 36° Y-cut X-propagation LiTaO₃ according to theexperiment. Hence, the equation (17) can be rewritten as follows:α=6.67×10⁻²/(4.22√{square root over (P)}−1)   (18).When P=1, then α=0.02, and Δf=19 MHz for the embodiment shown in FIG. 47having f_(rs) of 948 MHz. That is, the equation (18) stands.

An increase in Δf is effective for a piezoelectric substrate materialhaving a small capacitance ratio τ, that is a substrate material havinga large electromechanical coupling coefficient. The equation (17) isobtained for such a substrate material.

The capacitance ratio τ is proportional to the reciprocal of theelectromechanical coupling coefficient k². The value of the ratio τ for64° Y-cut X-propagation LiNbO₃ (k²=0.11) and the value of the ratio τfor 41° Y-cut X-propagation LiNbO₃ are respectively 6.8 and 4.4. Theabove values are obtained using the τ value of 36° Y-cut X-propagationLiTaO₃ and k²=0.05 (see K. Yamanouchi et al., “Applications forPiezoelectric Leaky Surface Wave”, 1990 ULTRASONIC SYMPOSIUMProceedings, pp.11-pp.18, 1990).

FIG. 53 shows the relation between the capacitance ratio τ and theelectromechanical coupling coefficient k², which is obtained using thevalues of k² and τ of 36° Y-cut X-propagation LiTaO₃ and using such arelation that k² is proportional to the reciprocal of τ.

From the relation shown in FIG. 53, the values of the capacitance ratiosτ of 64° and 41° Y-cut X-propagation LiNbO₃ substrates can be obtainedand are equal to 6.8 and 4.4, respectively.

The structure of the embodiment shown in FIGS. 44 and 45 will now bedescribed. The SAW filter 240 comprises a 36° Y-cut X-propagation LiTaO₃substrate 241, and has dimensions of 1.5 mm×2 mm×0.5 mm. From the inputside of the filter 240, a parallel-arm resonator Rp1, a series-armresonator Rs1, a parallel-arm resonator Rp2, a series-arm resonator Rs2,and a parallel-arm resonator Rp3 are arranged in that order. Each of theresonators has reflectors (short-circuit type) 242 respectively providedon both sides of the electrode having an aperture length of 180 μm and50 finger pairs. Each of the reflectors 242 has 50 finger pairs.

The parallel-arm resonators are the same as the series-arm resonatorsexcept for the periods of the interdigital electrodes. The period λ_(p)of the electrode of each parallel-arm resonator is 4.39 μm (the ratiobetween the pattern width and the gap is 1:1 and hence the pattern widthis approximately 1.1 μm (=λ_(p)/4), and the period of the electrode ofeach series-arm resonator is 4.16 μm (the pattern width is 1.04 μm(=λ_(s)/4)).

The respective periods are selected using the following equations sothat the resonance frequencies (f_(rp), f_(rs)) of the respectiveresonators are equal to the respective predetermined values (f_(rp)=893MHz, f_(rs)=942 MHz):λ_(s)=V_(m)/f_(rs)λ_(p)=V_(m)/f_(rp)where V_(m) is the sound velocity of the surface wave propagating in the36° Y-cut X-propagation LiTaO₃ crystal for an electrode thickness of3000 Å, and is experimentally 3920 m/s.

The SAW filter 240 having the above structure has a band-passcharacteristic having a broad pass band and a low loss, as shown in FIG.47C, in which Δf=19 MHz. When only the pattern width λ_(p) in FIG. 45 ischanged to 4.35 μm, then Δf becomes 10 MHz, and the characteristic shownin FIG. 47B is obtained. The electrode is made of an Al-Cu alloy and is3000 Å thick, and is arranged so that the surface wave is propagated inthe X direction of the piezoelectric substrate 241.

A description will now be given of piezoelectric substrates other than36° Y-cut X-propagation TiTaO₃. The capacitance ratio τ of 64° Y-cutX-propagation LiNbO₃ is 6.8, and an equation corresponding to theequation (17) is written as follows:α=1.47×10⁻¹/(4.37√{square root over (P)}−1)   (19)

The capacitance ratio τ of 41° Y-cut X-propagation LiNbO₃ is 4.4, and anequation corresponding to the equation (17) is written as follows:α=2.273×10⁻¹/(4.52√{square root over (P)}−1)   (20)As the τ value decreases, that is, the electromechanical couplingcoefficient increases, α increases, and the characteristic deteriorateslittle even if Δf increases.

A description will now be given of a twelfth embodiment of the presentinvention with reference to FIGS. 54 through 57. A SAW filter 250according to the twelfth embodiment of the present invention is aladder-type SAW filter having a plurality of basic units (unitsections), each having a SAW resonator in the parallel arm and a SAWresonator in the series arm, and establishes image impedance matchingbetween adjacent unit sections in order to reduce a loss at eachconnection node. With the above arrangement, it becomes possible toreduce the insertion loss in the pass band.

The twelfth embodiment of the present invention was made with thefollowing consideration. As shown in FIGS. 58A and 58B, a band-passcharacteristic can be obtained by means of at least one parallel-armresonator and at least one series-arm resonator. The ladder-typeconnection comprising one parallel-arm resonator and one series-armresonator is the unit section of the filter.

It is desirable that the resonance frequency of the series-arm resonatorbe equal to or higher than the antiresonance frequency of theparallel-arm resonator. Two unit sections respectively shown in FIGS.58A and 58B are available. The series arm of the unit section shown inFIG. 58A series serves as the input terminal, and the series arm of theunit section shown in FIG. 58B serves as the output terminal. Amulti-stage connection comprising a plurality of unit sections iscategorized into one of three types shown in FIGS. 59A, 59B and 59C.FIG. 59A shows an arrangement in which either the input or the output isa series arm and the other is a parallel arm (asymmetrical type). FIG.59B shows an arrangement in which both the input and output are parallelarms (symmetrical type). FIG. 59C shows an arrangement in which both theinput and output are series arms (symmetrical type).

The insertion loss of the multi-stage connection having n unit sectionsis n times that of the unit section, and the side lobe suppressionfactor thereof is also n times that of the unit section. Generally, theinsertion loss increases, while the side lobe suppression is improved.Particularly when the insertion loss is approximately zero, themulti-stage connection is an effective means. However, the insertionloss will be larger than n times that of the unit section unless theimpedance matching between the adjacent unit section is good. If theimpedance matching is poor, power is reflected at the interfaces betweenadjacent unit sections (each of the interfaces l-l′-n-n′). Thereflection of power increases the insertion loss. When the powerreflection occurring at an interface between adjacent unit sections isdenoted by Γ, the loss is expressed as n10log(Γ). Hence, it is importantto suppress increase in the insertion loss establishing an impedancematch between adjacent unit sections and suppressing power reflection ateach interface between two adjacent unit sections.

A descriptions will now be given of a method for matching the impedanceof adjacent unit sections. As shown in FIG. 60, when two circuits 1 and2, each having four different terminal constants (four parameters A, B,C and D of an F matrix), are connected to each other so that theimpedance matching therebetween is established, the circuits aredesigned so that image impedances obtained by viewing the circuits 1 and2 from an interface b-b′ are equal to each other. An image impedanceZ_(i1) obtained by viewing the circuit 1 from the impedance b-b′ can beexpressed as follows, using four terminal constants A₁, B₁, C₁ and D₁ ofthe circuit 1: $\begin{matrix}{Z_{i1} = {\sqrt{D_{1}{B_{1}/C_{1}}A_{1}}.}} & (21)\end{matrix}$Similarly, an image impedance Z_(i2) obtained by viewing the circuit 2from the interface b-b′ can be expressed as follows: $\begin{matrix}{Z_{i2} = {\sqrt{A_{2}{B_{2}/C_{2}}D_{2}}.}} & (22)\end{matrix}$The image impedances Z_(i1) and Z_(i2) are determined regardless of aload resistance (pure resistance) R₀.

When the equations (21) and (22) are equal to each other, the followingimpedance matching condition can be obtained:D₁B₁/C₁A₁=A₂B₂/C₂D₂   (23).

FIG. 61A shows a connection having poor impedance matching, and thecondition of the equation (23) is not satisfied. The reflection factor Γobtained by viewing the right circuit from the interface b-b′ isexpressed as follows:Γ=(Z_(s)Y_(p))/(2+Z_(s)Y_(p))   (24).The values of the Z_(s) and Y_(p) of a practical element are not equalto zero, and hence the reflection factor Γ thereof is not zero.

In a connection shown in FIG. 61B, an image impedance Z_(i1) obtained byviewing the left circuit from the interface b-b′ is obtained as follows,using the equation (21): $\begin{matrix}{Z_{i1} = {\sqrt{Z_{s}/{Y_{p}\left( {1 + {Z_{s}Y_{p}}} \right)}}.}} & (25)\end{matrix}$An image impedance Z_(i2) obtained by viewing the right circuit from theinterface b-b′ can be obtained using the equation (22). It will be notedthat Z_(i2)=Z_(i1). Hence, the impedance matching is established, andthe reflection factor Γ at the interface b-b′ is zero. The above holdstrue for a connection shown in FIG. 61C.

A description will now be given of a method for cascading a plurality ofunit sections in the manner shown in FIG. 61B or 61C. FIG. 62-(A) showsa circuit comprising n unit sections (n>2), in which the connectionmethod shown in FIG. 61B and the connection method shown in FIG. 61C arealternatively employed. It will be seen from the above description thatthere is no reflection at each interface.

The circuit shown in (A) of FIG. 62 can be modified, as shown in (B) ofFIG. 62, in which two resonators respectively in adjacent parallel nodesare integrated and two adjacent resonators in the series arm are alsointegrated. The series-arm resonator closest to the input of the filterhas an impedance value half that of the resonators located inside theabove series-arm resonator. Similarly, the parallel-arm resonatorclosest to the output of the filter has an admittance value half that ofthe resonators located inside the above parallel-arm resonator.

FIGS. 63A, 63B and 63C show configurations obtained by applying theabove modifying method shown in FIG. 62 to the configurations shown inFIGS. 59A, 59B and 59C, respectively. More particularly, FIG. 63A showsan impedance matching method corresponding to the matching method shownin FIG. 59A, in which either the input or output of the filter is theseries arm and the other is the parallel arm. In the configuration shownin FIG. 63A, the impedance of the series-arm resonator located at oneend of the filter is half that of each inner series-arm resonator, andthe admittance of the parallel-arm resonator located at the other end ofthe filter is half that of each inner parallel-arm resonator.

FIG. 63B shows an impedance matching method corresponding to thematching method shown in FIG. 59B. In the configuration shown in FIG.63B, each of two parallel-arm resonators located at respective endsthereof has an admittance value half that of the inner parallel-armresonator.

FIG. 63C shows an impedance matching method corresponding to thematching method shown in FIG. 59C. In the configuration shown in FIG.63C, each of the two series-arm resonators located at respective endsthereof has an impedance value half that of the inner series-armresonators.

A further description will now be given of the twelfth embodiment of thepresent invention based on the above-mentioned concept. The SAW filter250 according to the twelfth embodiment has the equivalent circuit shownin FIG. 54, and the practical structure shown in FIG. 55. As shown inFIG. 54, it has three series-arm resonators Rs1, Rs2 and Rs3, and threeparallel-arm resonators Rp1, Rp2 and Rp3. Each of the six resonators hasan identical aperture length (90 μm), and an identical number of fingerpairs (100). Each of the resonators has two short-circuit-typereflectors respectively located on two opposite sides of theinterdigital electrode in order to increase Q. Each of the reflectorshas approximately 100 finger pairs. The series-arm resonators Rs1, Rs2and Rs3 have an identical finger period (λ_(s)) of 4.191 μm. Theparallel-arm resonators Rp1, Rp2 and Rp3 have an identical finger periodλ_(p) of 4.38 μm, which is different from the value of λ_(s).

FIG. 64 shows a conventionalcomparative example of the SAW filterrelated to the SAW filter250 according to the twelfth embodiment of thepresent invention as a related art. In each of the filters shown inFIGS. 54 and 64, the design specification of each series-arm SAWresonator indicated by impedance Z_(s) is such that the aperture lengthis 90 μm and the number of finger pairs is 100. The design specificationof each parallel-arm SAW resonator indicated by admittance Y_(p) is thesame as the above design specification. The piezoelectric substratecrystal is made of 36° Y-cut X-propagation LiTaO₃. On the crystalsubstrate, an interdigital pattern for each SAW resonator formed with anAl alloy pattern having a thickness of 3000 Å is provided.

Curve 251 of the solid line shown in FIG. 56 indicates thecharacteristic of the filter 250. Curve 252 of the broken line shown inFIG. 56 indicates the characteristic of the filter shown in FIG. 64. Itcan be seen from FIG. 56 that the filter 250 has an insertion loss lessthan that of the filter shown in FIG. 64, and particularly the insertionloss at both ends of the pass band in the filter 250 is greatlyimproved.

Curve 253 shown in FIG. 57 shows a band characteristic of theconventional filter shown in FIG. 64, in which such an embodiment thatthe number of finger pairs of only the parallel-arm resonator indicatedby admittance Y_(p) is reduced from 100 to 80 to thereby reduce thevalue of the admittance Y_(p). It can be seen from FIG. 57 that theinsertion loss in the pass band is improved. It may be said that theinsertion loss can be somewhat improved even by reducing the admittanceof the resonator at the end of the filter by a quantity less than ½. Theabove holds true for impedance.

The embodiment based on the basic structure shown in FIG. 63A has beendescribed. A variation in which a number of unit sections are providedat the center of the filter has the same advantages as the aboveembodiment.

A description will now be given, with reference to FIG. 65, of a SAWfilter 260 according to a thirteenth embodiment of the presentinvention. The SAW filter 260 is based on the basic structure shown inFIG. 63B, and has the same insertion loss improvement as shown by thecurve 251 in FIG. 56.

FIG. 66 shows a SAW filter 270 according to a fourteenth embodiment ofthe present invention. The filter 270 is based on the basic structureshown in FIG. 63C. The filter 270 has the same insertion lossimprovement as shown by the curve 251 in FIG. 56.

FIGS. 67 and 68 show a SAW filter 280 according to a fifteenthembodiment of the present invention. The present embodiment is based onsuch a consideration that the insertion loss depends on a resistancecomponent and a conductance component of the interdigital electrode.With the above in mind, the fifteenth embodiment is intended to reducethe resistance component of each series-arm resonator and reduce theconductance component of each parallel-arm resonator and to therebyreduce the total insertion loss of a filter in which resonators make aladder-type connection.

Referring to FIG. 67, SAW resonators R_(s1), R_(s2) and R_(s3) areprovided in the series arm, and SAW resonators R_(p1), R_(p2) and R_(p3)are provided in the respective parallel arms. The resonance frequencyf_(rs) of each of the resonators in the series arm is different from theresonance frequency f_(rp) of each of the resonators in the parallelarms.

It will now be assumed that the admittance of each parallel-armresonator is expressed as follows:Y_(p)=g+j·b   (26)where g denotes a conductance component, and b denotes a susceptance.Further, it will be assumed that the impedance of each series-armresonator is expressed as follows:Z_(s)=r+j·x   (27)where r denotes a resistance component, and x denotes a reactancecomponent.

Under the above assumptions, the frequency characteristics of g, b, rand x are as shown in FIG. 71. The susceptance component b (indicated bythe dot chained line) of the admittance Y_(p) of the parallel-armresonator has the largest value at the resonance frequency f_(rp), atwhich the sign thereof changes from + to −. Further, the susceptancecomponent b becomes zero at the antiresonance frequency f_(ap), at whichthe sign thereof changes from − to +. The conductance component g(one-dot chain line) has the largest value is at the resonance frequencyf_(rp), and rapidly decreases and approaches zero. The value of theconductance component g assumes only the plus sign.

The reactance component x (indicated by the solid line in FIG. 71) ofthe impedance Z_(s) of the series-arm resonator becomes zero at theresonance frequency f_(rs), and the largest value at the antiresonancefrequency f_(as). Further, the sign of the reactance component x changesfrom + to −, and approaches zero from the minus side in a range higherthan f_(as). The resistance component r gradually increases from zero tothe largest value at the antiresonance frequency f_(as), and thengradually decreases. The resistance component r assumes only the plussign.

In order to obtain a filter characteristic, the antiresonance frequencyf_(ap) of the parallel-arm resonator is equal to or slightly smallerthan the resonance frequency f_(rs) of the series-arm resonator.

A graph depicted in the lower portion of FIG. 71 shows the bandcharacteristic of the filter circuit. The pass band is formed aroundf_(ap)≈f_(rs), and the other frequency range serves as an attenuationrange. It can also be seen from FIG. 71 that b and x are respectivelyzero around the center frequency of the pass band. Hence, the pass bandcharacteristic of the filter is determined by only r and g, and thefollowing is obtained:S21=100/(100+r+50r·g+2500 g)   (28).Since r>0 and g>0, S21 becomes smaller than 1 as both r and g increase,and the insertion loss written as 20log, ¦S21¦ also increases. Hence,the insertion loss decreases as both r and g are closer to zero.

A description will now be given of a consideration concerning which partof the interdigital electrode is related to the resistance component rand the conductance component g. The above consideration takes intoaccount a resistance r₁ inserted in the equivalent circuit shown in FIG.5B. The resistance r₁ is the sum of the electric resistance component ofthe interdigital electrode and an acoustic resistance componentcorresponding to an energy loss encountered while bulk waves generatedfrom ends of the fingers are propagated inside the substrate. Theresistance component resulting from emission of bulk waves is littledependent on the shape of the interdigital electrodes, and is henceproportional to the electric resistance r₁ of the interdigitalelectrode. Particularly, r=r₁ around the center frequency of x=0.

The conductance component g of the admittance of the parallel-armresonator is proportional to the conductance 1/r₁ of the electricresistance of the interdigital electrode.

The following equation is known:r=l_(s)·ρ_(O)/(N_(s)·W·t)   (29)where ρ_(O) denotes the resistivity of the fingers of the interdigitalelectrodes, W denotes the width of each finger, t denotes the filmthickness of each finger, l_(s) denotes the aperture length of theseries-arm resonator, and N_(s) denotes the number of finger pairs.

The conductance component g is obtained as follows if the same substrateand the same metallic film as those used in the series-arm resonator areemployed:g=N_(p)·W·t/(l_(p)·ρ_(O))   (30)where l_(p) denotes the aperture length of the parallel-arm resonator,and the N_(p) denotes the number of finger pairs. It will be noted thatρ_(O), W and t in the parallel-arm resonator are almost the same asthose in the series-arm resonator.

Hence, an increase in the insertion loss in the equation (28) isexpressed as follows:r+50r·g+2500g=l_(s)·ρ_(O)/(N_(s)·W·t)+50·(l_(s)/l_(p))·(N_(p)/N_(s))+2500·N_(p)·W·t/(l_(p)·ρ_(O)).  (31)

It can be seen from equation (31) that the insertion loss of theseries-arm resonator becomes smaller as the aperture length l_(s)decreases and the number N_(s) of finger pairs increases, and that theinsertion loss of the parallel-arm resonator becomes smaller as theaperture length l_(p) increase and the number N_(p) of finger pairsdecreases. Particularly, the insertion loss can be effectively reducedwhen l_(s)/l_(p)<1 and N_(p)/N_(s)<1, that is, when the aperture lengthof the series-arm resonator is smaller than that of the parallel-armresonator, and the number of finger pairs of the series-arm resonator islarger than the number of finger pairs of the parallel-arm resonator.

The reason for the above will now be described. In equation (31),r=r_(s) (r_(s): electric resistance of the series-arm resonator), andg=1/r_(p) (r_(p): electric resistance of the parallel-arm resonator),and therefore the following expression can be obtained:r+50r·g+2500 g=r_(s)+50(r_(s)/r_(p))+2500(1/r_(p)).Hence, an increase in the insertion loss can be suppressed when(r_(s)/r_(p))<1, that is, r_(s)<r_(p).

If l_(s) is too short, a loss resulting from diffraction of the surfacewave takes place. If l_(p) is too long, a decrease in Q of theparallel-arm resonator due to resistance increase appears, and the sidelobe suppression factor is deteriorated. Hence, there is a limit onl_(s) and l_(p).

The equation (31) can be modified as follows:r+50r·g+2500g=l_(s)·ρ₀/(N_(s)·W·t_(s))+50·(l_(s)/l_(p))·(N_(p)/N_(s))+(t_(p)·t_(s))+2500·N_(p)·W·t_(p)/(l_(p)·ρ_(O))  (32)where t_(s) denotes the film thickness of the metallic film forming theinterdigital electrode of the series-arm resonator, and t_(p) denotesthe film thickness of the metallic film forming the interdigitalelectrode of the parallel-arm resonator. Hence, the insertion loss canbe reduced when t_(p)/t_(s).

It is possible to use resonators, each having two different metallicfilms having different resistivity values (ρ_(os), ρ_(op)) and toarrange these resonators in the parallel and series arms, so thatρ_(op)/ρ_(op)<1 can be satisfied. However, this is not practical interms of mass productivity.

A further description will be given, with reference to FIGS. 67 and 68,of the fifteenth embodiment based on the above concept. A piezoelectricsubstrate 241 is formed of 36° Y-cut X-propagation LiTaO₃, and anelectrode is made of Al and 3000 Å thick.

Conventionally, in each of the parallel and series arms, l_(s)=l_(p)=90μm, and N_(p)=N_(s)=100. In the present embodiment, l_(s)=45 μm andN_(s)=200 in the series arm, while l_(p)=180 μm and N_(p)=50 in theparallel arm. That is, l_(p) >l _(s), and N_(s)>N_(p). Further,l_(s)/l_(p)=0.25, and N_(p)/N_(s)=0.25. The electrostatic C_(O) of theinterdigital electrode based on the product of the number of fingerpairs and the aperture length is kept constant.

In FIG. 69, solid line 281 indicates the characteristic of the presentembodiment, and broken line 282 indicates the characteristic of theconventional filter. The conventional filter has an insertion loss of2.5 dB, while the present embodiment has an insertion loss of 2.0 dB.That is, the insertion loss is improved by 0.5 dB, in other words, 25%.Further, since an increased number of finger pairs of the series-armresonator is used, the breakdown power performance is improved, and theapplicable maximum power is improved by 20%.

In the present embodiment, a diffraction loss appears when l_(s) isequal to or less than 30 μm, and them side lobe starts to deterioratewhen l_(p) is equal to or larger than 300 μm. Hence, the l_(s) and l_(p)are limited to the above values. It can be seen from the above that theinsertion loss in the pass band is improved by decreasing the electricresistance of the series-arm and increasing the electric resistance ofthe parallel arm (decreasing the conductance). It is also possible touse a parallel-arm resonator having a film thickness larger than that ofthe series-arm resonator. Even with this structure, it is possible toreduce the insertion loss in the pass band.

A description will now be given, with reference to FIG. 72, of a wavefilter according to a sixteenth embodiment of the present invention. Thewave filter (branching filter) shown in FIG. 72 comprises two SAWfilters F1 and F2 having input terminals connected to a pair of commonsignal terminals TO via common nodes a and b. The SAW filter F1 has apair of signal terminals T1, and the SAW filter F2 has a pair of signalterminals T2. A pair of signal lines l_(h) and l_(c) connects the nodesa and b to the SAW filter F1, and another pair of signal lines l_(h) andl_(c) connects the nodes a and b to the SAW filter

The SAW filter F1 comprises a series-arm SAW resonator Rso, and aparallel-arm SAW resonator Rp, which resonators are configured as hasbeen described previously. The resonator Rso is connected to the commonnode a, and hence serves as a resonator of the first stage of the SAWresonator F1. A plurality of pairs, each pair of series-arm resonatorand parallel-arm resonator are cascaded in the SAW filter F1. The SAWfilter F2 is configured in the same manner as the SAW filter F1.

The SAW filters F1 and F2 respectively have different band centerfrequencies. For example, the SAW filter F1 has a band center frequencyf₁ of 887 MHz, and the SAW filter F2 has a band center frequency f₂ of932 MHz. In this case, the frequency f₁ is lower than the frequency f₂.

FIG. 73 is a Smith's chart of the wave filter shown in FIG. 72. In FIG.72, P indicates the pass band of the wave filter. A indicates alow-frequency-side attenuation band, and B indicates ahigh-frequency-side attenuation band. It can be seen from FIG. 73 thatthe characteristic impedance of the circuit shown in FIG. 72 is equal to50 Ω, while the impedances of the attenuation bands A and B are greaterthan 50 Ω. This means that the wave filter shown in FIG. 72 has theimpedance characteristics of the respective band-pass filters.

A description will now be given, with reference to FIGS. 74 and 75, of awave filter according to a seventeenth embodiment of the presentinvention. In FIG. 74, parts that are the same as parts shown in thepreviously described figures are given the same reference symbols.

As has been described previously, the SAW filters F1 and F2 satisfy thecondition f₁<f₂. If the SAW band-pass filters F1 and F2 havecharacteristics as shown in FIG. 75, the filter F1 is maintained in ahigh-impedance state within the pass band frequency band of the filterF2. In this case, there is no need to provide an impedance matchingcircuit M to the filter F1, and the same characteristic as thecharacteristic of the filter F2 alone can be obtained.

However, the filter F2 does not have a high impedance within thelow-frequency attenuation band A thereof, and crosstalk may take place.Hence, it is necessary to increase the impedance within thelow-frequency attenuation band A of the filter F2.

An impedance matching circuit M for increasing the impedance in thelow-frequency attenuation band A thereof is connected between the nodesa and b and the filter F2. The impedance matching circuit M includes aninductor L, which is a high-impedance element for rotating the phase ofsignal. The inductor L has an inductance of, for example, 6 nH. Theinductor L can be formed with, for example, a metallic strip line madeof, for example, gold, tungsten, or copper, and formed on a glass-epoxyor ceramic substrate. The strip line formed on the glass-epoxy substratehas a width of 0.5 mm and a length of 11 mm, and the strip line formedon the ceramic substrate has a width of 0.2 mm and a length of 6 mm.

As shown in FIG. 75, the impedance matching circuit M provided for thefilter F2 rotates the phase in the direction indicated by the arrow, andthe impedance of the filter F2 in the low-frequency attenuation band Acan be increased.

FIG. 76 shows a wave filter according to an eighteenth embodiment of thepresent invention. In FIG. 76, parts that are the same as parts shown inthe previously described figures are given the same reference symbols.The wave filter shown in FIG. 76 can be obtained by connecting acapacitor C, which corrects the quantity of phase rotation of theinductor L, in series between the inductor L and the series-armresonator Rso. There is a possibility that a suitable impedance matchingmay be not obtained by means of only inductor L. As shown in a Smith'schart shown in FIG. 77, the phase is rotated in the direction indicatedby the arrow shown in FIG. 77 first, and is rotated by means of theinductor L second.

FIG. 78 shows a wave filter according to a nineteenth embodiment of thepresent invention. The filter F1 comprises the series-arm SAW resonatorRso and the parallel-arm SAW resonator Rp, which are connected so thatthe series-arm resonator is located at the first stage of the filter F1.The parallel-arm SAW resonator Rpo of the filter F is located at thefirst stage of the filter F. A line S for use in phase rotation isconnected in series to the SAW filter F2. It is possible to increase theimpedance of the filter F1 within the high-frequency attenuation band Bthereof even by an arrangement such that only the filter F1 has theseries-arm resonator of the first stage. In this case, the resonator ofthe first stage of the filter F2 is the parallel-arm resonator Rpoconnected in parallel to the pair of common signal terminals T0, and thelow-frequency attenuation band A of the filter F2 (corresponding to thepass band of the filter F1 does not have a high impedance. Hence,according to the present embodiment, the phase rotation line S isconnected in series to the filter F2.

As shown in FIG. 79, the direction of phase rotation caused by the lineS is opposite to the directions shown in FIGS. 75 and 77. However, asshown in FIG. 80, suitable matching of the filter F2 can be obtained. Inthis case, the length of the line S formed on the glass-epoxy substrateis approximately 25 mm, and the length of the line S formed on theceramic substrate is approximately 26 mm.

A variation of the configuration shown in FIG. 78 can be made byproviding the inductor L in the same manner as shown in FIG. 74. It isalso possible to further provide the capacitor C in the same manner asshown in FIG. 76.

The band center frequencies f₁ and f₂ of the sixteenth throughnineteenth embodiments of the present invention are not limited to 887MHz and 932 MHz.

The present invention is not limited to the specifically disclosedembodiments, and variations and modifications may be made withoutdeparting from the scope of the present invention.

1. A band-pass filter having a pair of band-pass filter input commonsignal terminals and plural pairs of band-pass filter output signalterminals, comprising: a pair of SAW band-pass filters having respectivepass bands and comprising a plurality of one-port SAW acoustic waveresonators connected in a multiple ladder structure, each having atleast a first stage located at a side of the pair of band-pass filterinput common signal terminals and a series-arm resonator located at thefirst stage, a pair of input terminals and a pair of output terminals;the pair of band-pass filter input common signal terminals beingcommonly connected to the respective pairs of input terminals of thepair pair of SAW band-pass filters; the plurality of pairs of band-passfilter output signal terminals being respectively connected to therespective pairs of output terminals of the pair pair of SAW band-passfilters; and an inductance element located between at least one side ofonly one of the SAW band-pass filters located at the first stage and thepair of band-pass filter input terminals and directly connected betweenthe respective pair of input terminals of the at least one of the SAWfilters and thereby in parallel to said at least one of the SAW filtersone of the common signal terminals, and no inductance element beinglocated between the other of the band-pass filters and one of the commonsignal terminals.
 2. A SAW filter comprising: a plurality of first SAWresonators, each having a pair of terminals and a predeterminedresonance frequency (f_(rp)), said first SAW resonators being connectedin respective, parallel arms of the SAW filter; a plurality of secondSAW resonators, each having a pair of terminals and a predeterminedresonance frequency (f_(rs)) approximately equal to an antiresonancefrequency (f_(ap)) of each of the first SAW resonators, said second SAWresonators being provided in series arms of the SAW filter; andinductance elements respectively connected in series with the first SAWresonators in the parallel arms and formed of wires.
 3. The SAW filteras claimed in claim 2, further comprising: a package accommodating thefirst and second resonators and the inductance elements; and leadterminals extending from interiorly of the package to exteriorlythereof, said wires of the inductance elements being bonded to said leadterminals.
 4. A band-pass filter having a predetermined pass-bandcharacteristic and comprising: a plurality of SAW resonators connectedin a ladder formation, said plurality of resonators being connected inrespective serial arms and parallel arms; and bonding inductanceelements, said parallel arms of said ladder formation being connected toground via respective said bonding inductance elements.
 5. The band-passfilter as claimed in claim 4, wherein said bonding inductance elementscomprise wires.
 6. A band-pass filter having a pair of band-pass filterinput terminals and plural pairs of band-pass filter output terminals,comprising: a pair of SAW filters having respective, different passbands and each SAW filter having a pair of SAW filter input terminalsand a pair of SAW filter output terminals and comprising a plurality ofone-port SAW resonators connected in a ladder structure between theinput and output terminals and including at least a first stage having aseries-arm SAW resonator connected to one of the pair of inputterminals; a pair of SAW filters having respective pass bands andcomprising a plurality of one-port SAW resonators connected in a ladderstructure, each having at least a first stage located at a side of thepair of band-pass filter input terminals and a series-arm resonatorlocated at the first stage, a pair of input terminals and a pair ofoutput terminals; the pair of band-pass filter input terminals beingcommonly connected to the respective pairs of input terminals of thepair of SAW filters; the plurality of pairs of band-pass filter outputterminals being connected to the respective pairs of output terminals ofthe pair of SAW filters.
 7. A band-pass filter having a predeterminedpass-band characteristic and comprising: a plurality of SAW resonatorsconnected in a ladder configuration of respective serial arms andparallel arms, said plurality of SAW resonators being connected inrespective said serial arms and parallel arms; and bonding inductanceelements respectively connecting said parallel arms of said ladderconfiguration to ground.
 8. An acoustic wave filter comprising: a firstacoustic wave resonator having a pair of terminals and a predeterminedresonance frequency (frp), said first acoustic wave resonator beingprovided in a parallel arm of the acoustic wave filter on a LiTaO ₃substrate; and a second acoustic wave resonator having a pair ofterminals and a predetermined resonance frequency (frs) approximatelyequal to a predetermined antiresonance frequency of the first acousticwave resonator (fap), said second acoustic wave resonator being providedin a series arm of the acoustic wave filter on the LiTaO ₃ substrate;and an inductance element connected in series with the first acousticwave resonator in the parallel arm, the inductance element functioningto increase the admittance of the parallel arm and decrease theresonance frequency, wherein the first acoustic wave resonator comprisesan exciting interdigital electrode and first and second reflectors, eachof which comprises either aluminum or an aluminum alloy containing a fewweight percentage of metal, other than aluminum; and the respective filmthicknesses of the exciting interdigital electrode and the first andsecond reflectors are in a range of from 0.06 to 0.09 times the periodof the exciting interdigital electrode.
 9. An acoustic wave filtercomprising: a first acoustic wave resonator having a pair of terminalsand a predetermined resonance frequency (frp), said first acoustic waveresonator being provided in a parallel arm of the acoustic wave filteron a LiTaO ₃ substrate; and a second acoustic wave resonator having apair of terminals and a predetermined resonance frequency (frs)approximately equal to a predetermined antiresonance frequency of thefirst acoustic wave resonator (fap), said second acoustic wave resonatorbeing provided in a series arm of the acoustic wave filter on the LiTaO₃ substrate; and an inductance element connected in series with thefirst acoustic wave resonator in the parallel arm, the inductanceelement functioning to increase the admittance of the parallel arm anddecrease the resonance frequency, wherein the first acoustic waveresonator comprises an exciting interdigital electrode and first andsecond reflectors, each of which comprises either gold or a gold alloycontaining a few weight percentage of metal other than gold; and therespective film thicknesses of the exciting interdigital electrode andthe first and second reflectors are in a range of from 0.0086 to 0.013times the period of the exciting interdigital electrode.
 10. An acousticwave filter comprising: a plurality of first acoustic wave resonators ona single piezoelectric substrate, each having a pair of terminals and apredetermined resonance frequency (frp), said first acoustic waveresonators being connected in respective, parallel arms of the acousticwave filter; a plurality of second acoustic wave resonators on thepiezoelectric substrate, each having a pair of terminals and apredetermined resonance frequency (frs) approximately equal to thepredetermined antiresonance frequency of the first acoustic waveresonator (fap), said second acoustic wave resonators being provided ina series arm of the acoustic wave filter; and inductance elementsrespectively connected to ground in series with the first acoustic waveresonators in the parallel arms.
 11. A band-pass filter having a pair ofband-pass filter common signal terminals and plural pairs of band-passfilter signal terminals, comprising: a first band-pass filter having apass band, having a band center frequency and comprising a plurality ofacoustic wave resonators connected in a multiple ladder structure,having at least a first stage located at a side of the pair of band-passfilter common signal terminals, a pair of input terminals and a pair ofoutput terminals; a second band-pass filter having a different pass bandfrom the pass band of the first band-pass filter, having a band centerfrequency which is larger than the band center frequency of the firstband-pass filter and comprising a plurality of acoustic wave resonatorsconnected in a multiple ladder structure, having at least a first stagelocated at a side of the pair of band-pass filter common signalterminals, a pair of input terminals and a pair of output terminals; thepair of band-pass filter common signal terminals being commonlyconnected to the first and second band-pass filters; the plurality ofpairs of band-pass filter signal terminals being respectively connectedto the first and second band-pass filters; and only one impedancematching circuit located only between the first stage of the secondband-pass filter and the common signal terminals.
 12. The band-passfilter as claimed in claim 11 , wherein the impedance matching circuitincludes an inductor.
 13. The band-pass filter as claimed in claim 12 ,wherein the inductor is formed with a metallic strip line.
 14. Theband-pass filter as claimed in claim 13 , wherein the metallic stripline is formed on a ceramic package.
 15. The band-pass filter as claimedin claim 11 , wherein said impedance matching circuit includes aninductor and a capacitor.
 16. A band-pass filter comprising: a firstband-pass filter having a pass band, having a band center frequency andcomprising a plurality of acoustic wave resonators connected in amultiple ladder structure, having at least a first stage and aseries-arm resonator located at the first stage, a pair of inputterminals and a pair of output terminals; a second band-pass filterhaving a different pass band from the pass band of the first band-passfilter, having a band center frequency which is larger than the bandcenter frequency of the first band-pass filter and comprising aplurality of acoustic wave resonators connected in a multiple ladderstructure, having at least a first stage and a parallel-arm resonatorlocated at the first stage, a pair of input terminals and a pair ofoutput terminals; a pair of band-pass filter common signal terminalscommonly connected to the first and second band-pass filters; aplurality of pairs of band-pass filter signal terminals respectivelyconnected to the first and second band-pass filters; a circuit elementused for phase rotation and connected between at least one of the pairof common signal terminals and the second band-pass filter.
 17. Theband-pass filter as claimed in claim 16 , wherein the circuit elementcomprises a line formed on a glass-epoxy substrate or a ceramicsubstrate.
 18. The band-pass filter as claimed in claim 16 , wherein thecircuit element comprises an inductance element.
 19. The band-passfilter as claimed in claim 18 , wherein the circuit element furthercomprises a capacitance element coupled to the inductance element.
 20. Aband-pass filter having a predetermined pass-band characteristic andcomprising: a plurality of acoustic wave resonators connected in aladder formation, said plurality of resonators being connected inrespective serial arms and parallel arms; and bonding inductanceelements, said parallel arms of said ladder formation being connected toground via respective said bonding inductance elements, wherein: apackage in which the band-pass filter is mounted, contains apiezoelectric substrate and the ground; and the plurality of acousticwave resonators are on the piezoelectric substrate.
 21. A band-passfilter having a predetermined pass-band characteristic and comprising: aplurality of acoustic wave resonators connected in a ladder formation,said plurality of resonators being connected in respective serial armsand parallel arms; and bonding inductance elements, said parallel armsof said ladder formation being connected to ground via respective saidbonding inductance elements, wherein: a package in which the band-passfilter is mounted contains a piezoelectric substrate; the plurality ofacoustic wave resonators are on the piezoelectric substrate; and a firstelectric resistance (Rs) of an interdigital electrode of a acoustic waveresonator provided in a series arm, is smaller than a second electricresistance (Rp) of an interdigital electrode of a acoustic waveresonator provided in a parallel arm which is next to the series arm.22. A band-pass filter having a predetermined pass-band characteristicand comprising: a plurality of acoustic wave resonators connected in aladder formation, said plurality of resonators being connected inrespective serial arms and parallel arms; and bonding inductanceelements, said parallel arms of said ladder formation being connected toground via respective said bonding inductance elements, wherein: theplurality of acoustic wave resonators are on a piezoelectric substrate;and the bonding inductance elements are respectively connected to theground outside the piezoelectric substrate.